## Why I am not a Bayesian

6 January, 2019 at 19:30 | Posted in Theory of Science & Methodology | 2 CommentsNo matter how atheoretical their inclination, scientists are interested in relations between properties of phenomena, not in lists of readings from dials of instruments that detect those properties …

Here as elsewhere, Bayesian philosophy of science obscures a difference between scientists’ problems of hypothesis choice and the problems of prediction that are the standard illustrations and applications of probability theory. In the latter situations, such as the standard guessing games about coins and urns, investigators know an enormous amount about the reality they are examining, including the effects of different values of the unknown factor. Scientists can rarely take that much knowledge for granted. It should not be surprising if an apparatus developed to measure degrees of belief in situations of isolated and precisely regimented uncertainty turns out to be inaccurate, irrelevant or incoherent in the face of the latter, much more radical uncertainty.

Although Bayesians think otherwise, to me there’s nothing magical about Bayes’ theorem. The important thing in science is for you to have strong evidence. If your evidence is strong, then applying Bayesian probability calculus is rather unproblematic. Otherwise — garbage in, garbage out. Applying Bayesian probability calculus to subjective beliefs founded on weak evidence is not a recipe for scientific progress. It is important not to equate science with statistical calculation or applied probability theory. All science entail human judgement, and using statistical models doesn’t relieve us of that necessity. Statistical models are no substitutes for doing real science. Although Bayesianism has tried to extend formal deductive logic into real-world settings via probability theory, this is not a viable scientific way forward. Choosing between theories and hypotheses can never be a question of inner coherence and consistency. Bayesian probabilism says absolutely nothing about reality.

Rejecting probabilism, Popper not only rejects Carnap-style logic of confirmation, he denies scientists are interested in highly probable hypotheses … They seek bold, informative, interesting conjectures and ingenious and severe attempts to refute them.

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Is anyone a Bayesian in the sense that Miller seems to suppose? Does he add anything to previous critiques? As a mathematician, I would tend to trust Ramsey, de Finetti and Savage to a psychologists interpretation of probability theory,

I commend the following critique of the kind of Bayesianism that Miller supposes:

“[This discussion, in contrast to naïve induction] demonstrates, particularly, that instead of proving that events will always happen agreeably to it, there will be always reason against this conclusion. In other words, where the course of nature has been the most constant, we can have only reason to reckon upon a recurrency of events proportioned to the degree of this constancy, but we can have no reason for thinking that there are no causes in nature which will ever interfere with the operations the causes from which this constancy is derived, or no circumstance of the world in which it will fail.”

Bayes (Ed. Price) An Essay towards solving a Problem in the Doctrine of Chances 1763

I have similar quotes from Ramsey, de Finetti and Savage on my blog djmarsay.wordpress.com. In particular, Savage notes that whereas naïve applications are reasonable for what he calls ‘small worlds’, many worlds are ‘large’. In effect, mainstream economists assume that economies are ‘small worlds’, but Lars presumably thinks them large (as did Keynes and as do I). So I find Miller’s criticism of Ramsey et al unfounded.

Its as if we blamed the makers of chain saws because some people misuse them, ignoring the user instructions.

Comment by Dave Marsay— 7 January, 2019 #

Dave, as you note, “mainstream economists assume that economies are ‘small worlds’, but Lars presumably thinks them large (as did Keynes and as do I)” And that’s a very important point, totally in line with what Miller argues. And as Deborah Mayo forcefully has argued in her latest books, science is not only (not even mainly) about probability — and that kind of probabilism has always been typical of Bayesian confirmation and inference theory!

Comment by Lars Syll— 8 January, 2019 #